# 10 by wanghonghx

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```									       Lecture 10
Potential Energy

 Potential   Energy
Definition
Conservative Forces

 Conservation   of Energy

 Power
Work Done by Gravity
 Wg   = -mgy
Independent of path (only depends on
initial and final height)
If you end up where you began, Wg = 0
Define: Potential Energy: Ug = mgy
Thus: Ug = mgy = -Wg

We call gravity a “Conservative Force” because Wg
is path independent (and therefore we can define a
“Potential Energy” to go with it).
Potential (stored) Energy
   Works for any CONSERVATIVE force
Gravity Ug = m g y
Spring Us = ½ k x2
NOT friction

   “Stored” Gravitational Energy can be
converted to Kinetic Energy
Wg= K
-m g y = K
0 = K + m g y
0 = K + Ug
Work - Energy w/ Conservative Forces

Work-Energy Theorem:
W  K
Move work by conservative forces to other side:
Wnc  K  U
If there are NO non-conservative forces:
0  K  U
Ki  U i  K f  U f
Power (Rate of Work)
P   = W / t
Units: Joules/Second = Watt (W)

 But   Remember:
W = F x cosq = F (v t) cosq
P = F v cosq
Summary
Conservative Forces
» Work is independent of path
» Define Potential Energy U
 Ugravity = m g y

 Uspring = ½ k x2

Work – Energy Theorem

Wnc  K  U
Example
   Standing at the top of a cliff you throw a ball at
12 m/s. If the cliff is 87 m high, how fast is the
ball moving right before it hits the ground?

We will use the Work-Energy Theorem:

Wnc  K  U
Example
   Standing at the top of a cliff you throw a ball at
12 m/s. If the cliff is 87 m high, how fast is the
ball moving right before it hits the ground?

0  K  U
Ki  U i  K f  U f
Example
   Standing at the top of a cliff you throw a ball at
12 m/s. If the cliff is 87 m high, how fast is the
ball moving right before it hits the ground?

1 2           1 2
mvi  mgyi  mv f  mgy f
2             2
cancel m from each expression
vi = 12 m/s
yi = 87 m
yf = 0 m
solve for vf
Example
   Standing at the top of a cliff you throw a ball at
12 m/s. If the cliff is 87 m high, how fast is the
ball moving right before it hits the ground?

Vf = 43 m/s

Notes:

The final speed did not depend on the angle the
ball was thrown upward (although the angle
would affect how quickly the ball hits the ground).

The mass of the ball did not affect the final speed.

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